Answer:
x=-6
Step-by-step explanation:
-18x=108
/-18. /-18
x=-6
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Divide both sides by −18.
x = 108/-18Divide 108 by −18 to get −6.
x=−6Fractions DIDES Change this improper fraction to a mixed number. Click OK when you are done. ME 10 6 Question 3 out of 10 TUTOR-EXERCISE | what is 10 over 6 as a improper fraction??
The improper fraction of [tex]\frac{10}{6}[/tex] is [tex]1\frac{2}{3}[/tex] .
Converting [tex]\frac{10}{6}[/tex] into improper fraction,
[tex]\frac{10}{6}\\\\=\frac{5}{3}[/tex]
Divide 5 by 3, we get 1 with remainder 2
Now, write 1 as whole number , 2 as new numerator and denominator remains same i.e. 3
Now, Improper fraction is [tex]1\frac{2}{3}[/tex] .
Thus, the improper fraction of [tex]\frac{10}{6}[/tex] is [tex]1\frac{2}{3}[/tex] .
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A merchant offers a large group of items at 18% off. later, the merchant takes 10% off these price sales and claims that the final price of these items is 86 off the original price. what is the total percent discount?
26.2% is the total percent of discount offered by the merchant.
Let us assume that each item is $100.
As it is given that 18% is off, we have an amount after off is:
Amount after 18% off = 100 × (100 - 18)/ 100
= 100 × 0.82
= 82
Next, there is 10% off
So the amount become = 82 ×( 100 - 10) / 100
= 82 ×0.9
= 73.8
So the final price of an item is $73.8
The discount = (100 - 73.8) / 100
= 26.2%
Therefore the total percent of discount is 26.2%.
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how many copies for every 10 minutes
Find the equation of the linear function represented by the table below in slope-
intercept form.
The equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.
What is an equation of a line?
A line's equation is a single representation of all of the line's points. The general form of a line equation is ax + by + c = 0, and each point on the line satisfies this equation. The slope of the line and a point on the line are the two necessary components to create the equation of a line.
The equation of a line, in the slope-intercept formula:
y = mx + b
In which,
m is the slope, that is, how much y changes when x changes by 1.
b is the y-intercept, that is, the value of y when x = 0.
Given two points (x,y), the slope is the change in y divided by the change in x.
We have points (-1, -2) and (1, -4).
[tex]m = \frac{(-2 - (-4))}{1 - (-1)}[/tex]
m = 1;
Then,
y = 1x + b
Point (-1,-2) means that when x = -1 and y = -2, we use this to find b.
y = 1x + b
-2 = 1(-1) + b
b = -2 + 1
b = -1
Thus,
y = x -1.
Hence, the equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.
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help with this math problem
The solution of the linear equation:
(2x + 6)/5 = 4x - 3
is x = 7/6
How to solve the equation?
Here we have the following equation:
(2x + 6)/5 = 4x - 3
To solve this, we need to isolate x in one of the sides of the equation, we can start by multiplying both sides by 5.
2x + 6 = 5*(4x - 3)
Expanding the right side we get:
2x + 6 = 20x - 15
Now you can see that this is a simple linear equation, now we need to group like terms:
6 + 15 = 20x - 2x
21 = 18x
Now we can divide both sides by 18 to get:
21/18 = x
Finally, if we divide both numerator and denominator of the fraction by 3, we get:
21/3 = 7
18/3 = 6
Then 21/18 = 7/6
Finally, we conclude that the solution is:
x = 7/6
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A delivery truck has 4 stops to make in a neighborhood. How many different sequences of stops can the driver make?
The number of different sequences of stops that the driver can make is 24.
What is permutation?Permutation is simply used it illustrate the number of ways for a given information. The formula is illustrated as:
n! / (n – r)!
N is the number of things you are choosing from,
r is the number of items.
“!” is a factorial of a number
Since the delivery truck has 4 stops to make in a neighborhood, the sequences of stops will be:
= n! / (n – r)!
= 4!
= 4 × 3 × 2
= 24 stops.
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A. 17 B. 117 C. 163 D. 173 In the figure above, n || p. Straight line m intersects both line n and line p. What is the value of r?
Y=1/2x+5
Y= -5/2x-1 ???
Answer:
It's correct
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: (-2, 4) Equation Form : X= -2, Y = 4.
a) What is the area of the shape below?
The area of the shape is 32 square yards
The given consist of one rectangle and a right triangle
The area of the figure = The area of the rectangle + The area of the right triangle
The area of the rectangle = The length × The width
The length of the rectangle = 6 yards
The width of the rectangle = 4 yards
The area of the rectangle = 6×4
= 24 square yards
The area of the triangle = (1/2)bh
The base of the triangle = 9 - 5 = 4 yards
The height = 4 yards
The area = (1/2)× 4 × 4
= 8 square yards
The area of the figure = 24 + 8
= 32 square yards
Hence, the area of the shape is 32 square yards
The complete question is:
What is the area of the shape below?
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The speed of light is about 3 × 105 kilometers per second. The distance between Earth and the Moon is about 3.84 × 105 kilometers. Find how long it would take for light to travel from Earth to the Moon.
In scientific notation
The time it would take for light to travel from Earth to the moon is; 1.28 seconds.
How long would it take to travel from Earth to the moon?It follows from the task content that the time it would take for light to travel from Earth to the Moon is to be determined.
Since the given speed of light is; 3 × 10⁵ km/s and the distance is; 3.84 × 10⁵ km.
It follows from the formula;
Speed = Distance / Time
Time = Distance/Speed
Time = 3.84 × 10⁵ / 3 × 3.10⁵
Time = 1.28 seconds.
Therefore, the required time it would take to travel from Earth to the moon is; 1.28 seconds.
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Two cars are traveling in the same direction. the first car is going 40 mi/h and the second car is going 55 mi/h. the first car has a 120 mile head start. which equation could you solve to find how many hours it will take for the second car to catch up to the first car?
The equation that could solve how many hours it will take for the second car to catch up to the first car is 55t = 120 + 40t.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
If the first car is going 40 mi/h, and has a 120 mile head start, then the distance it covers at time = t is,
d1 = 120 + 40t
If the second car is going 55 mi/h, you want to know the amount of time it will catch the first car, then, their distance must be equal.
d2 = 55t
d1 = d2
120 + 40t = 55t
Simplify the equation of t.
55t - 40t = 120
15t = 120
t = 8
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in a field hockey championship, 120 matches were played. every pair of team played one match with each other. the number of teams in the tournament is therefore:
The number of teams in the field hockey championship tournament is 16.
The total number of matches played in the field hockey championship are 120 matches.
Each pair of team played one match with each other.
So, let us say that there are N teams in the tournament.
So, we can chose any two teams for a match,
So, applying the permutation formula,
ⁿC₂ = 120
Solving further,
N!/2!(N-2)! = 120
N(N-1)/2 = 120
N(N-1) = 240
On observing closely and applying hit and trial method,
16(15) = 240
So, the values of N is 16.
Hence, 16 teams participated in the tournament.
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1/4(12k-4) ''simplify''
Using the distributive property, the simplified form of the expression 1/4(12k-4) is 3k-1.
In the given question we have to simplify the given expression.
The given expression is 1/4(12k-4).
To simplify the given expression we use the distributive property.
According to property; a(b+c) = ab+bc
Now simplifying the expression;
1/4(12k-4) = 1/4*12k-1/4*4
1/4(12k-4) = 3k-1
Hence, the simplified form of the expression 1/4(12k-4) is 3k-1.
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Verify that the function satisfies the three hypotheses of Rolle’s Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s theorem. (Enter your answers as a comma-separated list.) f(x) = x^3 - 4x^2 - 16x + 8, [-4,4] Find c =
There are no values within the interval that satisfies the condition stated by Rolle's theorem.
What numbers does satisfy Rolle's theorem?In accordance to Rolle's theorem, a function existing within an closed interval [a, b] has at a least a value c within that interval such that the first derivative f'(c) is equal to the slope of the secant line that passes through the two interval limits. That is to say, Rolle's theorem is defined by the following formula:
f'(c) = [f(b) - f(a)] / (b - a), where a < c < b
Where:
f(a), f(b) - Values of the function evaluated at each interval limit.f'(c) - First derivative of the function evaluated at x = c.First, evaluate the function f(x) at x = - 4:
x = - 4
f(- 4) = (- 4)³ - 4 · (- 4)² - 16 · (- 4) + 8
f(- 4) = - 64 - 64 + 64 + 8
f(- 4) = - 56
Second, evaluate the function f(x) at x = 4:
x = 4
f(4) = 4³ - 4 · 4² - 16 · 4 + 8
f(4) = 64 - 64 - 64 + 8
f(4) = - 56
Third, determine the first derivative of the function f(x) and evaluate it at x = c:
f(x) = x³ - 4 · x² - 16 · x + 8
f'(x) = 3 · x² - 8 · x - 16
x = c:
f'(c) = 3 · c² - 8 · c + 16
Fourth, find the roots of the quadratic function found in the previous step.
3 · c² - 8 · c + 16 = 0
In accordance with the quadratic formula, the roots of the expression are 4 / 3 + i 4√2 / 3 and 4 / 3 - i 4√2 / 3, which are not real numbers.
Fifth, determine whether Rolle's theorem are applicable on the roots found in the previous step.
Since the roots of the polynomial 3 · c² - 8 · c + 16 are not real numbers, there are no number within the interval that satisfies Rolle's theorem.
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maggie owes billy $14, her mother $45 and her sister $32. if Maggie has $100 in her purse and pays everyone back, how much money will maggie have left over
If maggie owes billy $14, her mother $45 and her sister $32. if Maggie has $100 in her purse and pays everyone back then 9 is the money maggie have left over
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
maggie owes billy $14
Maggies mother $45
Maggies sister $32
Maggies has $100 in her purse and pas everyone bills, we need to find how much money will maggie have left over
To do this we have to add all the bills and subtract from 100
Fourteen plus forty five plus thirty two
14+45+32
Ninety one
91
Now subtract 91 from 100.
100-91
9
Hence, $9 is the money will maggie have left over
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Isabel works 180 hours in one month.what is her average hourly wage,in dollars,to meet the budget?round to the nearest cent
One method is to determine the average hourly rate for all employees, regardless of where they work in your company, what they do, or how many hours they work.
How to Calculate the Average Hourly Rate for Employees ?To begin, calculate the total number of hours worked by multiplying the number of weeks in a year by the number of hours worked per week. Divide this figure by the annual salary. For example, if an employee earns $50,000 per year and works 40 hours per week, his or her hourly rate is $50,000/2,080 (40 x 52) = $24.04.
When budgeting for future projects, keep in mind that if you pay Bill $18 per hour, Lisa $16, and Hank and Jake $14, your labor costs will vary depending on who you send to the job site.
However, if you can use Bill less frequently each week and Hank or Jake more frequently, you might be able to budget for next month using the $15.82 per hour figure.
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A toy company puts 25 toy cars in each box.
How many toy cars are in 1,000 boxes? Use the expression 25 × 1,000 to find the answer. Then, describe the value of 25 in the result.
A. 2,500
The place value of 25 increases by 1 place to the left.
B. 2,500
The place value of 25 increases by 2 places to the left.
C. 25,000
The place value of 25 increases by 3 places to the left.
D. 25,000
The place value of 25 increases by 4 places to the left.
The number of toy cars are in 1,000 boxes is 25000 and the place value of 25 increases by 4 places to the left.
How to calculate the value?It should be noted that place value is used to know the value of the numbers that are given in a data.
In this case, toy company puts 25 toy cars in each box, the number of toy cars that are in 1,000 boxes will be:
= 25 × 1000
= 25000
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taking π=22/7, find the circumference of a circle 70cm
The circumference of circle of radius 70 cm is 440 [tex]cm^{2}[/tex].
According to the question,
We have the following information:
Radius of the circle = 70 cm
(Diameter is twice that of its radius..)
We know that the following formula is used to find the circumference of circle:
Circumference of circle = 2πr
(More to know: the formula to find the area of circle is π[tex]r^{2}[/tex].)
(More to know: there are two values of π. One is 3.14 and one is 22/7.)
Circumference of circle = 2*(22/7)*70
Circumference of circle = 440 [tex]cm^{2}[/tex]
Hence, the circumference of the circle of radius 70 cm is 440 [tex]cm^{2}[/tex].
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PLSSS HELP IF YOU TURLY KNOW THISS
Step-by-step explanation:
we have 11k + 4k.
this is like saying "I have 11 apples and then get 4 more apples - how many apples do I have ?"
in other words, how many "k" do I have ?
11 + 4 = 15.
we have 15k.
and then there is -3 + 8 = 5
so, the answer is
15k + 5
Answer:
15k + 5
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ 11k - 3 + 4k + 8
Let's simplify the expression,
→ 11k - 3 + 4k + 8
→ 11k + 4k - 3 + 8
→ (11k + 4k) + (-3 + 8)
→ (15k) + (5)
→ 15k + 5
Hence, the answer is 15k + 5.
Deshaun's gas tank is 1/10 full. After he buys 6 gallons of gas, it is 2/5 full. How many gallons can Deshuan's tank hold?
Answer:
20 gallons
Step-by-step explanation:
2/5 = 4/10
3/10 = 6 gallons
1/10 = 6 : 3= 2 gallons
10/10 = 2 * 10 = 20 gallons
Plot the x- and y-intercepts to graph the equation. y = 1/3x + 1
The graph that shows the x- and y-intercepts to graph the equation. y = 1/3x + 1 is added as an attachment
How to plot the equation on a graph?From the question, we have the following equation that can be used in our computation:
y = 1/3x + 1
We set x = 0 to determine the y-intercept
So, we have
y = 1/3 x 0 + 1
Evaluate
y = 1
So, we have
(x, y) = (0, 1)
We set y = 0 to determine the x-intercept
So, we have
0 = 1/3x + 1
Evaluate
1/3x = -1
This gives
x = -3
So, we have
(x, y) = (-3, 0)
So, the intercepts are (0, 1) and (-3, 0)
See attachment for the graph
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9) For a job, Phillippa is paid three times as much as Peter. Pavin is paid £10 more than Phillippa, Write an algebraic expression for the total of everyone's wages
Answer:
Step-by-step explanation:
Peter=x
Phillippa= 3x then x
Palvin= 10 then Phillippa
Step 2: Answer: Phillipa 3x+x+10
each law firm in one state registers its phone number with the state court system. an employee of the state court system uses a computer to select 500500500 random registered phone numbers, and the law firms associated with those numbers will be selected for an audit. what type of sample is this?
In this "Simple Random Sample" scenario, 500500500 selected randomly registered phone numbers were chosen.
Define the term Simple random sample?A subset of either a population is chosen at random in a basic random sampling. Each individual in the population has had an exact equal probability of getting selected using this sampling technique.Among all of the probability sampling techniques, this one is the easiest to understand because it only includes one random selection and little prior population knowledge. Any research conducted on this sample must have excellent validity both internally and externally because it uses randomization.For the given data in the question.
Every law firm in a state registers it phone number only with state court system as a result.Thus, 500500500 random registering phone numbers are randomly chosen by a state court employee using a computer, and the law firms connected to all those numbers are randomly chosen for an audit.
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Kareem cannot decide which of two washing machines to buy. The selling price of each is 600$. The first is marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each washing machine. Use pencil and paper. Explain why should buy the first washing machine rather than the second if the machines are the same except for the selling price.
The selling price of the first washing machine is $300
The selling price of the second washing machine is $336
The first washing machine appear to have more savings in cost
How to determine the selling prices of the two machinesThe question is a percentage problem
The first is marked down by 50%
= 50 percent
= 50 / 100
= 0.5
marked down factor = 1 - 0.5 = 0.5
selling price of the first machine = 600 * 0.5 = 300
Similarly the second selling washing machine has mark down of 30%
30% = 0.3
marked down factor = 1 - 0.3 = 0.7
selling price of the second washing machine at first mark down
= 600 * 0.7 = 420
second mark down
20% = 0.2
marked down factor = 1 - 0.2 = 0.8
selling price of the second washing machine at second mark down
= 420 * 0.8 = 336
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What is the slope of the line that
passes through these two points?
(-1,4)
(2,2)
Answer:
-2/3
Step-by-step explanation:
y2-y1/x2-x1
2-4/2-(-1)
-2/2+1
-2/3
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The hypotenuse of a right triangle measures 8 cm and one of its legs measures 4 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
4√3 (about 6.9) cm.
Step-by-step explanation:
In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
Here, the length of the longer leg is 4√3, or about 6.9, cm.
A school had 1 200 students last year and only 1 080 students this year.
What was the percent decrease in the number of students?
Answer:The percentage decrease in the number of students is -10%.
Given that,
The school has 1,200 students last year.
And, this year it is 1,080.
Based on the above information, the calculation is as follows:
Therefore we can conclude that the percentage decrease in the number of students is -10%.
Step-by-step explanation: noice
Suppose each data value in a data set is multiplied by 8. What will
happen to the mean?
Select one:
- It will be 4 times as much.
- It will increase by 4.
- It will be 8 times as much.
It will increase by 8, as well.
The fraction is equivalent to which of the following decimal numbers?
0.2
0.1616
0.166
0.1 6
The fraction of 1/6 is equivalent to this following decimal number:
0.166.
How to convert a fraction to a decimal number?A fraction is represented by the division of a term x by a term y, as follows:
Fraction = x/y.
The terms that represent x and y are given as follows:
x, which is the top term of the fraction, is called the numerator.y, which is the bottom term of the fraction, is called the denominator.In this problem, the fraction is given as follows:
1/6.
1 is less than 6, hence the equivalent decimal can be obtained as follows:
0.10/6.
10 divided by 6 is one with a remainder by 4, hence 1.4/6 = 1.6667.
Thus the equivalent decimal representing the fraction 1/6 is given as follows:
1/6 = 0.1666.
Missing informationThe problem asks for which decimal number the fraction 1/6 is equivalent.
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bruce bought two books.one book costs $4 more than three times than the other.they both equal 72$
Bruce paid $17 and $55 respectively for each of the books
How to determine the cost of each book?From the question, we have the following statements:
Number of books = 2One book = $4 more than three times the other.Both books = 72$Represent the books with the variables x and y
So, we have the following equations
x = 4 + 3y
x + y = 72
To start with;
We can substitute 4 + 3y for x in the equation x + y = 72
So, we have the following representation
4 + 3y + y = 72
Evaluate the like terms
4 + 4y = 72
Collect the like terms in the above equation
So, we have the following equation
4y = 72 - 4
Evaluate the like terms
4y = 68
Divide both sides by 4
So, we have
y = 17
Recall that x = 4 + 3y
Substitute 17 for y in the equation x = 4 + 3y
x = 4 + 3 * 17
Evaluate the products
x = 4 + 51
Evaluate the sum
This gives
x = 55
Hence, the cost of the books are $17 and $55
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Possible question
Bruce bought two books, one book costs $4 more than three times than the other. They both equal $72.
What is the cost of each book